Extremal and optimal properties of B-bases Collocation Matrices
Numerical Analysis
2024-12-20 v1 Numerical Analysis
Abstract
Totally positive matrices are related with the shape preserving representations of a space of functions. The normalized B-basis of the space has optimal shape preserving properties. B-splines and rational Bernstein bases are examples of normalized B-bases. Some results on the optimal conditioning and on extremal properties of the minimal eigenvalue and singular value of the collocation matrices of normalized B-bases are proved. Numerical examples confirm the theoretical results and answer related questions.
Cite
@article{arxiv.1901.09768,
title = {Extremal and optimal properties of B-bases Collocation Matrices},
author = {Jorge Delgado and J. M. Peña},
journal= {arXiv preprint arXiv:1901.09768},
year = {2024}
}
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11 pages